Two Banks (Franklin and Lincoln)compete for Customers in the Growing $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Lincoln Bank }$

question 60

Essay

Two banks (Franklin and Lincoln)compete for customers in the growing city of Logantown.Both banks are considering opening a branch office in one of three new neighborhoods: Hillsboro,Fremont,or Oakdale.The strategies,assumed to be the same for both banks,are:
Strategy 1: Open a branch office in the Hillsboro neighborhood.
Strategy 2: Open a branch office in the Fremont neighborhood.
Strategy 3: Open a branch office in the Oakdale neighborhood.
Values in the payoff table below indicate the gain (or loss)of customers (in thousands)for Franklin Bank based on the strategies selected by the two banks. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Lincoln Bank }$
$\begin{array}{|c|ccc|}\hline\text{Franklin Bank}&\begin{array}{c}\text { Hillsboro } \\b_{1}\end{array} & \begin{array}{c}\text { Fremont } \\b_{2}\end{array} & \begin{array}{c}\text { Oakdale } \\b_{3}\end{array} \\\hline \text{Hillsboro }a_{1} &4 & 2 & 3 \\\text{Fremont }a_{2} &6 & -2 & -3 \\\text{Oakdale }a_{3} &-1 & 0 & 5 \\\hline\end{array}$ Identify the neighborhood in which each bank should locate a new branch office.What is the value of the game?

---

Definitions:

Standard Deviation

A metric assessing how much a batch of values differs or spreads out.

Sampling Distribution

The probability distribution of a statistic obtained from a large number of samples drawn from a specific population.

Sample Size

The number of observations or dataset elements selected from a population for the purpose of statistical analysis.

Sample Means

The average value of a set of samples from a population.